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Home » c = 2R \sin\left(rac heta2 - Fine VPN

c = 2R \sin\left(rac heta2 - Fine VPN

📅 May 13, 2026 👤 scraface

May 13, 2026

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📌 Use quadratic formula: \( t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \)

📌 \( a = -5, b = 20, c = 2 \)

📌 Discriminant: \( 20^2 - 4(-5)(2) = 400 + 40 = 440 \)

📌 \( t = \frac{-20 \pm \sqrt{440}}{-10} = \frac{-20 \pm 2\sqrt{110}}{-10} = \frac{20 \mp 2\sqrt{110}}{10} = 2 \mp \frac{\sqrt{110}}{5} \)

📌 Only positive root: \( t = 2 + \frac{\sqrt{110}}{5} \approx 2 + 1.05 = 3.05 \) seconds.

📌 Problem:** The sum of the first \( n \) terms of an arithmetic sequence is \( S_n = 3n^2 + 5n \). What is the 10th term?

📌 The \( n \)-th term \( a_n = S_n - S_{n-1} \).

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